What does lambda tell you about the relationship between two variables?

What does lambda tell you about the relationship between two variables?

• A. The extent to which one variable predicts the other; 1 means perfect prediction
• B. The strength of linear correlation
• C. The probability of independence
• D. The variance explained by the model

Answer: (A)

Lambda tells you how much one variable helps you predict the other when both are categorical. It’s the proportionate reduction in prediction error you get when you use the first variable to predict the second, compared with just guessing the most frequent category. If the value is 1, you can predict perfectly every time; if it’s 0, knowing one variable gives you no better prediction than always guessing the most common category. This is different from the strength of a linear relationship (which uses numeric data and yields a correlation coefficient), from a probability of independence (which is about testing whether variables are independent), and from the amount of variance explained (which comes from regression and ANOVA concepts). So lambda specifically reflects predictive power between two categorical variables, with 1 meaning perfect prediction.

Lambda tells you how much one variable helps you predict the other when both are categorical. It’s the proportionate reduction in prediction error you get when you use the first variable to predict the second, compared with just guessing the most frequent category. If the value is 1, you can predict perfectly every time; if it’s 0, knowing one variable gives you no better prediction than always guessing the most common category.

This is different from the strength of a linear relationship (which uses numeric data and yields a correlation coefficient), from a probability of independence (which is about testing whether variables are independent), and from the amount of variance explained (which comes from regression and ANOVA concepts). So lambda specifically reflects predictive power between two categorical variables, with 1 meaning perfect prediction.